Question

In the graph, the area below f(x) is shaded and labeled A, the area below g(x) is shaded and labeled B, and the area where f(x) and g(x) have shading in common is labeled AB.

the graph represents which system of inequalities?

y<-3x-1 y<-x-4

y>-3x+1. y<-x-4

y<3x-1. y<-x-4

y<3x-1. y>-x+4

help pls

Answer 1

The graph represents the system of inequalities y < 3x - 1 and y <= -x + 4.

How derive equation of line of an inequality line.

Given the line equations f(x) and g(x)

Let's find the equation of the line using the graph and the formula of the line passing two points,

Equation of line is

y = mx + b

m is slope

b is y-intercept

For f(x)

y-intercept = -1

Locate points (0, -1) and (2,5)

m = 5 -(-1)/2-0

= 6/2 = 3

y = 3x - 1

below the line is shaded

y < 3x - 1

For g(x)

y-intercept = 4

Locate points (4,0) and (0,4)

m = -4-0/4-0

= 4/4 = -1

y = -x + 4

below is shaded and the boundary line is included

y <= -x + 4

The graph represents the system of inequalities y < 3x - 1 and y <= -x + 4.